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About the author

Aliakbar Montazer Haghighi, PhD, is Professor and Head of the Department of Mathematics at Prairie View A&M University, USA, as well as founding Editor-in-Chief of Applications and AppliedMathematics: An International Journal (AAM). His research interests include probability, statistics, stochastic processes, and queueing theory. Among his research publications and books, Dr. Haghighi is the coauthor of Difference and Differential Equations with Applications in Queueing Theory (Wiley, 2013).

Dimitar P. Mishev, PhD, is Professor in the Department of Mathematics at Prairie View A&M University, USA. His research interests include differential and difference equations and queueing theory. The author of numerous research papers and three books, Dr. Mishev is the coauthor of Difference andDifferential Equations with Applications in Queueing Theory (Wiley, 2013).

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Presents an introduction to differential equations, probability, and stochastic processes with real-world applications of queues with delay and delayed network queues

Featuring recent advances in queueing theory and modeling, Delayed and Network Queues provides the most up-to-date theories in queueing model applications. Balancing both theoretical and practical applications of queueing theory, the book introduces queueing network models as tools to assist in the answering of questions on cost and performance that arise throughout the life of a computer system and signal processing. Written by well-known researchers in the field, the book presents key information for understanding the essential aspects of queues with delay and networks of queues with unreliable nodes and vacationing servers.

Beginning with simple analytical fundamentals, the book contains a selection of realistic and advanced queueing models that address current deficiencies. In addition, the book presents the treatment of queues with delay and networks of queues, including possible breakdowns and disruptions that may cause delay. Delayed and Network Queues also features:

Numerous examples and exercises with applications in various fields of study such as mathematical sciences, biomathematics, engineering, physics, business, health industry, and economics

A wide array of practical applications of network queues and queueing systems, all of which are related to the appropriate stochastic processes

Up-to-date topical coverage such as single- and multiserver queues with and without delays, along with the necessary fundamental coverage of probability and difference equations

Discussions on queueing models such as single- and multiserver Markovian queues with balking, reneging, delay, feedback, splitting, and blocking, as well as their role in the treatment of networks of queues with and without delay and network reliability

Delayed and Network Queues is an excellent textbook for upper-undergraduate and graduate-level courses in applied mathematics, queueing theory, queueing systems, probability, and stochastic processes. The book is also an ideal reference for academics and practitioners in mathematical sciences, biomathematics, operations research, management, engineering, physics, business, economics, health industry, and industrial engineering.

Aliakbar Montazer Haghighi, PhD, is Professor and Head of the Department of Mathematics at Prairie View A&M University, USA, as well as founding Editor-in-Chief of Applications and AppliedMathematics: An International Journal (AAM). His research interests include probability, statistics, stochastic processes, and queueing theory. Among his research publications and books, Dr. Haghighi is the coauthor of Difference and Differential Equations with Applications in Queueing Theory (Wiley, 2013).

Dimitar P. Mishev, PhD, is Professor in the Department of Mathematics at Prairie View A&M University, USA. His research interests include differential and difference equations and queueing theory. The author of numerous research papers and three books, Dr. Mishev is the coauthor of Difference andDifferential Equations with Applications in Queueing Theory (Wiley, 2013).

5.8 Single-Server Queue with Unreliable Server and Breakdowns with an Optional Second Service, 222

5.9 A Bulk Arrival Retrial Queue with Unreliable Server, 229

5.9.1 The Model, 231

5.9.2 Model Analysis, 233

5.9.3 Steady-State System Analysis, 237

5.9.4 Performance Measures, 244

5.9.5 Numerical Illustration, 248

5.10 Multiserver Queue with Retrial Feedback Queuing System with Two Orbits, 253

5.11 Steady-State Stability Condition of a Retrial Queuing System with Two Orbits, Reneging, and Feedback, 258

5.11.1 Necessary Stability Condition for the Steady-State System, 259

5.12 Batch Arrival Queue with General Service in Two Fluctuating Modes and Reneging During Vacation and Breakdowns, 263

5.12.1 The Model, 263

5.12.2 Analysis, 265

Exercises, 266

6 Networks of Queues with Delay 267

6.1 Introduction to Networks of Queues, 267

6.2 Historical Notes on Networks of Queues, 270

6.3 Jackson's Network of Queues, 272

6.3.1 Jackson's Model, 273

6.4 Robustness of Networks of Queues, 298

6.5 A MAP Single-Server Queueing System with Delayed Feedback as a Network of Queues, 302

6.5.1 Description of the Model, 304

6.5.2 Service Station, 307

6.5.3 Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case When Batch Sizes Vary Between a Minimum k and a Maximum K, 319

6.6 Unreliable Networks of Queueing System Models, 336

6.6.1 Unreliable Network Model of Goodman and Massey, 337

6.6.2 Unreliable Network of Queues Model of Mylosz and Daduna, 340

6.6.3 Unreliable Network of Queues Model of Gautam Choudhury, Jau-Chuan Ke, and Lotfi Tadj: A Queueing System with Two Network Phases of Services, Unreliable Server, Repair Time Delay under N-Policy, 348